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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 4290v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4290.u4 | 4290v1 | \([1, 1, 1, 65, -235]\) | \(30342134159/47190000\) | \(-47190000\) | \([4]\) | \(2048\) | \(0.15774\) | \(\Gamma_0(N)\)-optimal |
| 4290.u3 | 4290v2 | \([1, 1, 1, -435, -2835]\) | \(9104453457841/2226896100\) | \(2226896100\) | \([2, 2]\) | \(4096\) | \(0.50432\) | |
| 4290.u1 | 4290v3 | \([1, 1, 1, -6485, -203695]\) | \(30161840495801041/2799263610\) | \(2799263610\) | \([2]\) | \(8192\) | \(0.85089\) | |
| 4290.u2 | 4290v4 | \([1, 1, 1, -2385, 41625]\) | \(1500376464746641/83599963590\) | \(83599963590\) | \([2]\) | \(8192\) | \(0.85089\) |
Rank
sage: E.rank()
The elliptic curves in class 4290v have rank \(0\).
Complex multiplication
The elliptic curves in class 4290v do not have complex multiplication.Modular form 4290.2.a.v
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
